Assume that...

(9/18/2008 12:00:00 AM)

Assume that

... the ancient philosophers were correct in that the earth is indeed flat. Set the premise that the earth is an infinitely large slab with a finite thickness, h. What is the value of h (expressed in terms of Earth Radii) such that a person standing on the slab would experience the same gravitational acceleration as he/she would, standing on earth now?

The slab is of the same density as earth (assume homogeneous), and you can assume too, that the force pulling the person sideways would cancel out eventually, (although there is a way to mathematically prove that it would).

I have managed to evaluate the integral with my father's help. The solution is extremely elegant! If you feel you haven't accomplished much in your life, or that the world is woe and weary, you must at least attempt this question to do some good to society before you resign into decadence.

I can assure you solving this would be a cathartic pleasure.

The answer is 2/3 R by the way. The solution is entirely within J1 syllabus. It, however, requires some thinking when you try to express dm (infinitesimal mass unit) in terms of rho (density) and dv (infinitesimal volume). <-- hint

If you are unable to solve it and would like the solution, or if you are just plain lazy, you could always approach me. ~ming.